Answer
False.
Work Step by Step
Let $h(x)=f(x)\times g(x)$ and $f'(x)gt;0; g'(x)gt;0$ over some interval $(a, b).$
Then $h'(x)=f'(x)g(x)+g'(x)f(x)$ which is not necessarily positive over the interval $(a, b)$ since we do not know the values of $f(x)$ and $g(x).$
